1333:

Piast Poland, 966 to 1370
A very clean black and white map depicting the boundaries of Poland at the death of Boleslaw the Brave in 1025 and during the reign of Kazimierz the Great, 1333-70. From the Library of Congress Country Study on Poland, online here at the Medieval History site.

1340:

Map of South Eastern Europe
From the Atlas to Freeman's Historical Geography, edited by J.B. Bury, a map focusing on the political divisions of the Balkans and other portions of southeastern Europe, here at the Medieval History site.

1346:

Political Map of Europe
This map of Europe just before the arrival of the Black Death was created by your guide and is available right here at the Medieval History site.

1348:

Spread of the Black Death, Jan.-June
This map depicting the course the Black Death took in Europe in the first half of 1348 was created by your guide and is available right here at the Medieval History site.

Spread of the Black Death, Jul.-Dec.
This map depicting the course the Black Death took in Europe in the second half of 1348 was created by your guide and is available right here at the Medieval History site

1349:

Spread of the Black Death, 1349
This map depicting the course the Black Death took in Europe in 1349 was created by your guide and is available right here at the Medieval History site.

1350:

Map of the Baltic Lands
A map depicting the lands bordering the Baltic Sea, including Russia, Scandinavia and Northern Europe, in the years 1350 to 1360. From the Atlas to Freeman's Historical Geography, online here at the Medieval History site.

1354:

Map of South Eastern Europe - 1354-1358
From the Atlas to Freeman's Historical Geography, edited by J.B. Bury, a map focusing on the political divisions of the Balkans and other portions of southeastern Europe from the year 1354 to 1358, here at the Medieval History site.

1360:

Map of Central Europe
From the Atlas to Freeman's Historical Geography, edited by J.B. Bury, a map of the political divisions of Germany and Central Europe, here at the Medieval History site.

Map of the Spanish Kingdoms
From the Atlas to Freeman's Historical Geography, edited by J.B. Bury, a map of the political divisions of the Iberian peninsula, here at the Medieval History site.

1390:

Muromachi Shugo c. 1390
Very large, attractive map of Japan at the Samurai Archives site. 

1400:

Map of the Byzantine Empire
Black and white map by Peter Dykhuis at ByzNet shows the borders of the empire.

Map of the Baltic Lands
A map depicting the lands bordering the Baltic Sea, including Russia, Scandinavia and Northern Europe. From the Atlas to Freeman's Historical Geography, online here at the Medieval History site.